Moderate deviation analysis of majorization-based resource interconversion
- Publication Type:
- Journal Article
- Citation:
- Physical Review A, 2019, 99 (3)
- Issue Date:
- 2019-03-22
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© 2019 American Physical Society. We consider the problem of interconverting a finite amount of resources within all theories whose single-shot transformation rules are based on a majorization relation, e.g., the resource theories of entanglement and coherence (for pure-state transformations), as well as thermodynamics (for energy-incoherent transformations). When only finite resources are available we expect to see a nontrivial trade-off between the rate rn at which n copies of a resource state ρ can be transformed into nrn copies of another resource state σ, and the error level ϵn of the interconversion process, as a function of n. In this work we derive the optimal trade-off in the so-called moderate deviation regime, where the rate of interconversion rn approaches its optimum in the asymptotic limit of unbounded resources (n→∞), while the error ϵn vanishes in the same limit. We find that the moderate deviation analysis exhibits a resonance behavior which implies that certain pairs of resource states can be interconverted at the asymptotically optimal rate with negligible error, even in the finite n regime.
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